378435 ÷ 42 
Let's see how many times 42 fits into 378435.

Advancing to step 1:
42 can be fit into 3 0 times, resulting in a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 42

Moving on to step 2:
42 can be fit into 37 0 times, resulting in a remainder of 37.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 37 and we're left with 37.
Take the next digit (8) from the dividend and append it to 37, then repeat: 378 / 42

Advancing to step 3:
42 goes into 378 9 times with a remainder of 0.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
Subtract 378 from 378 to get 0.
Grab the next digit (4) from the dividend, add it to 0, then carry on: 4 / 42

Going ahead to step 4:
The number 42 fits into 4 0 times, leaving a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 90.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 42

Advancing to step 5:
42 can be fit into 43 1 times, resulting in a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 901.0
Deduct 42 from 43 and we're left with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 42

Going ahead to step 6:
42 can be fit into 15 0 times, resulting in a remainder of 15.
Record the quotient 0 as the next digit in the result. 
Result so far: 9010.0
Deduct 0 from 15 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 7:
When dividing 150 by 42, we get 3 with a remainder of 24.
The next digit of our result is 3. 
Result so far: 9010.3
Deduct 126 from 150 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 8:
42 can be fit into 240 5 times, resulting in a remainder of 30.
The number 5 becomes the next digit in our result. 
Result so far: 9010.35
Deduct 210 from 240 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 9:
The number 42 fits into 300 7 times, leaving a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 9010.357
If we subtract 294 from 300, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 10:
The number 42 fits into 60 1 times, leaving a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 9010.3571
Subtracting 42 from 60 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 11:
180 divided by 42 is 4 with a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 9010.35714
Subtract 168 from 180 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 12:
When dividing 120 by 42, we get 2 with a remainder of 36.
Write down 2 as next digit of the result. 
Result so far: 9010.357142
If we take 84 away from 120, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 13:
360 divided by 42 is 8 with a remainder of 24.
Record the quotient 8 as the next digit in the result. 
Result so far: 9010.3571428
If we take 336 away from 360, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 14:
42 goes into 240 5 times with a remainder of 30.
The number 5 becomes the next digit in our result. 
Result so far: 9010.35714285
Deduct 210 from 240 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The final result is 9010.35714285 with a remainder of 3e-08.